Problem:
Algebra-Functions and Equations (InterMath)

Melanie is shopping for work clothes.

She has found a dress for \$75 and a two-piece suit for only \$60. She does not have enough money for both, so she must choose only one.

Of course, both are "dry clean only."

If her dry cleaner charges \$4.50 for a dress and #3 for each piece of suit, which will be a better deal in the long run?

How many times will she have to dry clean the purchased item before it is the better deal?

Solution:

x= number of times the garment is dry-cleaned
f(x)= 4.50x + 74
g(x) = 6x + 60

Set the two equations equal to each other and you get a point of intersection.

This point of intersection is where the garments would be costing the same amount in the "long run."

4.5x + 75 = 6x + 60
4.5x + 15 = 6x
15 = 1.5 x
10 = x

At the 10th dry cleaning the garments would cost exactly the same.

After that point, the dress (which originally cost more) would be more economical and financial friendly. :)

Melanie would have to dry clean her chosen item 11 times to make the dress the better deal in the long run.

Solution shown graphically:

This solution shows that the two garments would cost exactly the same at the 10th dry cleaning also...because you cannot dry clean an item 9.33 times...you must round up from 9 to 10.

The answer still remains that Melanie would have to dry clean her chosen item 11 times to make the dress the better deal in the "long run."